# Calculate volume of hydrogen gas evolved

MCQ Question:

Ammonia borane in water can release hydrogen upon hydrolysis while forming NH4BO2 as the other product.

The volume (cm3) of hydrogen gas which will be evolved from the hydrolysis of 309 mg of ammonia borane (NH3BH3) with a purity of 90 % w/w at 27 °C and at atmospheric pressure 1.0 bar is approximately,

(a) 66.5 cm3

(b) 224.5 cm3

(c) 673.4 cm3

(d) 893.2 cm3

(e) none of the above

The answer from the mark scheme is C) 673.4 cm3

I took the reaction equation as

NH3BH3 + 2 H2O -> NH4BO2 + 3 H2

However I cannot figure out how to attempt this question. What method should I follow to get 673.4 cm3 of hydrogen gas?

• Have you tried the ideal gas state equation pV=nRT? Commented Feb 5, 2023 at 16:31
• Transform the initial data into moles. Multiply by 3 to get the amount of H2. Hopefully you know why 3. Then apply pV = nRT to get the final volume V. Commented Feb 5, 2023 at 17:23
• Consider ammonia borane is the limiting reagent in the balanced equation. Thant gives you the $n$ in $pV = nRT$. What you don't know is only $V$. Commented Feb 5, 2023 at 17:24

NH3BH3 + 2H2 -> NH4BO3 + 3H2

309mg = 0.309g - use moles = mass/molar mass equation:

mol(NH3BH3) = 0.309/14+6(1)+10.8 = 0.309/30.8 = 0.01mol

Use stochiometric ratio 1:3 to recognize that you multiply the moles of NH3BH3 by 3 to get moles of H2, 0.01mol * 3 = 0.03mol = mol(H2)

Prepare variables for pV = nRT (pressure in Pa * volume in m^3 = 8.314 * moles of gas (H2) * temperature in kelvin) , rearranging equation to give V = nRT/p

To convert degrees C into Kelvin, add 273: 27 + 273 = 300K

To convert "bar" into Pa - one "bar" = 100000Pa

R is ideal gas constant 8.314

Substitute values into equation V = (0.03) * (8.314) * (300) / (100000) = 7.48 * 10^-4 m^3

Convert m^3 into cm^3 by multiplying by 1 million 7.48 * 10^-4 m^3 = 748.26cm^3

The 'purity' thing implies that only 90% of the calculated value is the answer - 784.26 * 0.9 = 673.4cm^-3 which is the answer.